9.10 The Laws of Thermodynamics
347
Q
1
H ≥ Q
2
H
(9.34)
making
E 1
E 2
≤ 1 ,
(9.35)
i.e. the reversible engine (number 2) is never less efficient than any other engine. If
both are reversible, then reversing both engines inverts the relation, so that only the
equality can apply:
E
rev
1
= E
rev
2
(9.36)
If all reversible engines have the same efficiency (irrespective of how they are
made), then the efficiencies can only depend on the temperatures of the reservoirs:
E rev = E rev (T H , T C ) , and not on what materials the engines are made from or how
the engines are constructed.
Now imagine coupling two reversible engines in series, as in Fig. 9.4. Let Q be
the heat transferred from the first to the second engine. Then energy conservation
gives
Q H = Q + W 1
(9.37)
Q = Q C + W 2
(9.38)
so the efficiency of the two is
Fig. 9.4 Stacked Carnot
engines
347
Q
1
H ≥ Q
2
H
(9.34)
making
E 1
E 2
≤ 1 ,
(9.35)
i.e. the reversible engine (number 2) is never less efficient than any other engine. If
both are reversible, then reversing both engines inverts the relation, so that only the
equality can apply:
E
rev
1
= E
rev
2
(9.36)
If all reversible engines have the same efficiency (irrespective of how they are
made), then the efficiencies can only depend on the temperatures of the reservoirs:
E rev = E rev (T H , T C ) , and not on what materials the engines are made from or how
the engines are constructed.
Now imagine coupling two reversible engines in series, as in Fig. 9.4. Let Q be
the heat transferred from the first to the second engine. Then energy conservation
gives
Q H = Q + W 1
(9.37)
Q = Q C + W 2
(9.38)
so the efficiency of the two is
Fig. 9.4 Stacked Carnot
engines